One-Tank Offline Learning

This example identifies a one-step predictor from a simulated water-tank trace. It uses the same system definition and simulation as the incremental learning variant, while training each model from a fixed dataset.

System and Data

The water level \(x\) follows

\[ \dot{x} = \frac{b V(t) - a \sqrt{x}}{A}, \]

where \(A = 5\) is the tank area, \(a = 0.5\) is the outflow rate, \(b = 2\) is the inflow rate, and

\[ V(t) = \max\left(0, \sin\left(2 \pi t / 10\right)\right). \]

examples/one_tank/system.py is the single source of this simulation. one_tank_system() represents the dynamics as a one-location HybridSystem with no transitions, and simulate_one_tank() returns a deterministic trace sampled from 0 to 25 seconds at 0.1-second intervals.

Both learning variants consume the resulting t and h columns. A three-sample SlidingWindow creates h_0, h_1, and h_2; the learners predict h_2 from the two preceding levels h_0 and h_1.

Offline Workflow

run_offline.py performs these steps:

1. Simulate the shared one-tank HybridSystem.
2. Apply a three-sample sliding window.
3. Shuffle and split the fixed data into 80 percent training and 20 percent test observations with seed 42.
4. Train a regression tree, a PyTorch multilayer perceptron, and a two-tree ensemble with learn_offline.
5. Evaluate each model with mean absolute error, mean squared error, and maximum error.

The script prints training times and evaluation reports. Reported values can vary across platforms and ML backend versions.

Run

From the repository root:

uv run --directory ./examples/one_tank python run_offline.py

To run both the offline and incremental variants:

just examples-one_tank

See the Hybrid Systems guide for the simulation model and Learning Strategies for offline learning concepts.